tzibur community - who says "baruch hu uvaruch sh'mo" before birkas hamazon

Ashk'nazi prayer books generally include the line

ברוך הוא וברוך שמו

after the zimun (invitation to say birkas hamazon and before the actual birkas hamazon. It generally (in my experience) is preceded by the instruction:

יחיד אינו אומר

yachid eno omer, which means "an individual does not say" or "someone alone does not say"; the word yachid is often used to refer to someone not part of a minyan.

Who should say this, and who should not — and why?

Ideas that come to mind are:

• Anyone included in a zimun should say it, but not someone saying birkas hamazon without a zimun.


• Anyone saying birkas hamazon with another says it, but not someone alone.


• Anyone included in a zimun of a minyan says it, but not someone saying birkas hamazon without a minyan.



• Anyone leading a zimun (the m'zamen) says it, but no one else.

I'd appreciate any argument or, especially, source. Naturally, for practical guidance, each person should rely on his rabbi rather than answers here.

Answer

Many thanks to Menachem who, in a comment on the question, gave references to some of the following, which led me also to the others:

• The Avudraham (Abudirham) says that only the leader of a zimun (the m'zamen) says it, and has a different nusach (wording): Baruch hu uvaruch zichro l'olme ad. (Many thanks to Menachem for finding this!)


• The Tur, OC 192 (and all citations below are to OC 192), mentions saying baruch hu uvaruch sh'mo. It seems to me from his language that he holds that it's only said when there's a zimun, and only by the leader (m'zamen). Others comment that it's not mentioned in the g'mara, Rosh, Rif, or Rambam, but that the L'vush and Rokeach (284) also mention it — but I haven't looked them up.
  
  
  
  • The Rama (in Darke Moshe :2) holds not to say it.
  
  
  
  • The Bach seems to hold (if I understand him correctly) that those answering to a zimun of a minyan say it, but no one in a smaller (or no) zimun.
  
  
  • The P'risha (:2) holds (if I understand him correctly) that only the leader (m'zamen) says it.
  
  
  
  


• The Shulchan Aruch and Rama (in the Mapa) make no mention of baruch hu uvaruch sh'mo. Nor does the Taz. The Magen Avraham and Baer Hetev comment that the Shulchan Aruch holds that we don't say it.
  
  
  
  • The Magen Avraham himself (:0), however, notes the common practice is to say it, and adds that one should not say it without a zimun.
  
  
  • And Baer Hetev himself (:3) says that the common practice is to say it when there's a zimun. He doesn't seem to say who should say it when there's a zimun, though I suspect that he'd follow the Tur and others cited above and hold that only the leader (m'zamen) says it.
  
  
  • The Shaare S'shuva says that no one but the leader of a zimun (the m'zamen) should say it.
  
  
  
  
  


• The Shulchan Aruch Harav (:2) notes that some have the practice of saying it, and adds in parentheses that no one but the leader of a zimun (the m'zamen) should say it.


• The Aruch Hashulchan (:5) says that it's appropriate to omit baruch hu uvaruch sh'mo and that that's the common practice.


• The Mishna B'rura (:4) says it's said only with a zimun, and only by the leader (m'zamen).
  
  
  
  • The Shaar Hatziyun (:3) says that the G'ra holds not to say it.